Ferro-nano-carbon split ring resonators a bianisotropic metamaterial in X-band: Constitutive parameters analysis

Accepted Manuscript Ferro-nano-carbon split ring resonators a bianisotropic metamaterial in X-band: Constitutive parameters analysis Resham V. Jagtap, Ashok D. Ugale, Prashant S. Alegaonkar PII:

S0254-0584(17)30906-9

DOI:

10.1016/j.matchemphys.2017.11.027

Reference:

MAC 20147

To appear in:

Materials Chemistry and Physics

Received Date: 25 April 2017 Revised Date:

6 October 2017

Accepted Date: 13 November 2017

Please cite this article as: R.V. Jagtap, A.D. Ugale, P.S. Alegaonkar, Ferro-nano-carbon split ring resonators a bianisotropic metamaterial in X-band: Constitutive parameters analysis, Materials Chemistry and Physics (2017), doi: 10.1016/j.matchemphys.2017.11.027. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Ferro-nano-carbon Split Ring Resonators a Bianisotropic Metamaterial in X-band:

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Constitutive Parameters Analysis

Resham V Jagtap, Ashok D Ugale, and Prashant S Alegaonkar

Department of Applied Physics, Defence Institute of Advance Technology, Girinagar, Pune 411025, MS, India

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Abstract

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We report on preparation and evaluation of constitutive parameters for ferro-nano-carbon (FNC) split ring resonators (SRRs) behaving as a bianisotropic left-handed material (LHM) that generated an electromagnetic cloak in sub-X-band region (8.5-10 GHz). Initially, FNC was synthesis by pyrolysis of 1,7,7-trimethyl-bicycloheptan incorporated with variable wt % (3-20) of cobalt. Morphological studies showed spherically concentric shells (40-50 nm) of FNC

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interconnected spatially. In Raman, FNC vibration modes indicated encaging of Co-sp3 phase

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within sp2 shells, whereas, dielectric studies revealed low-frequency orientational polarization attributed to chair-to-chair sp2 segmental motion surrounding Co-sp3 fraction. In VSM, higher

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exchange anisotropy emerged in FNC due to randomly spaced, smaller concentration of Co-

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structural inhomogeneities interacted, indirectly, within carbon super-lattice. The FNCs were implemented into SRRs to investigate microwave scattering response, experimentally. The constitutive parameters were extracted and, comparatively, studied using Nicolson-Ross-Weir and retrieval technique. Analysis of obtained results is presented. Scattering (S)-parameters and fields were simulated, indicating S11 around - 20 and S21 ~ 0 dB, at 8.5 GHz with concealing of 

Corresponding author: P S Alegaonkar, [email protected], [email protected]

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incident field at SRRs cell. The resemblance of simulated S-parameters with experimental values is discussed. Broadly, out of phase response of Co-sp3 dipolar fields segregated charges in opposite direction to harmonically oscillating incident magnetic field. This resulted into

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bianisotropic LHM behavior of FNC when transformed into SRRs; generating a cloak like

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response, particularly, at 8.5-10 GHz.

Abbreviation: SRRs, split ring resonators; FNC, ferro-nano-carbon; LHM, left handed material;

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VSM, vibrating sample magnetometer; FESEM, field emission scanning electron microscopy; HRTEM, high resolution transmission electron microscopy; EDAX, energy dispersive spectroscopy.

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material; electromagnetic cloak.

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Keywords: Ferro-nano-carbon; split ring resonators; constitutive parameters; left handed

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1. Introduction

The threat spectrum of a tracking radar comprises of surveillance, guidance, and homing mode.

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In general, the tracking trail of a target due to its interaction with microwave (radar) radiations is assumed to be, strategically, hostile activity. There are several penetration aids like radar absorbing material, booster fragmentation, jammers, chaff, decoys, etc. to clutter or shield the

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signature of such object [1]. In recent years, cloaking techniques have been emerged as a promising countermeasure to make the target invisible! [2]. In this, the paths of electromagnetic

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waves are controlled within a material by introducing a specific spatial variations in (constitutive parameters) permeability (µ) and permittivity (ɛ) [3,4]. The cloak architecture involves coordinate transformation of constitutive parameters that squeezes incident field space volume into a shell surrounding the concealing volume; achieved via a cellular pattern. The pattern obeys , where, a is periodic dimension of the pattern, λ, incident

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a scattering condition:

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wavelength, ω, frequency of radiation, and c, velocity of light[5]. Physically, incoming wave field gets coupled to the cellular pattern to pop-up magnetic or electric dipole, at the cell,

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depending upon charge dynamics within the pattern. This causes asymmetric reflection, or asymmetric transmission, or complete concealing of the incident field. Thus, cloaking effect

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comes under the category of metamaterial, which is exotic having negative constitutive parameters, not necessary for cloaking, however, useful for wave propagation in backward direction, zero-point phase velocity, and offers negative refractive index to the medium. Formally, Veselago [6] proposed metamaterial, also popularly, known as negative index material (NIM), or LHM [7]. For normal medium, achieving metamaterial properties is challenging due to restrictive values of constitutive parameters because of myopic response of atoms and molecules 3

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to the incident radiation. For cellular architecture, the field behavior could be studied by analyzing tensors of permittivity, permeability, chiral parameter, nonreciprocity conditions, forward/backward reflections, scattering (S)-parameters (or impedances), scattering power,

an anisotropic, bianisotropic, and/or chiral metamaterials.

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reflection coefficient, magnetoelectric coupling factors, refractive index, etc., to classify them as

The first theoretical realization of LHM occurred in studying a wired metallic medium whose

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permittivity was estimated to be negative due to artificial electric plasma properties of the medium [8]. By constructing metal split ring resonators (SRRs), the magnetic plasma properties

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of cellular medium were manipulated to achieve negative permeability. The first artificial LHM was demonstrated by Smith et.al. in 2001 by combining metal wires and SRRs in which phenomenon of the negative refraction was confirmed [9]. In recent years, LHM has been the focus of both theoretical exploration and experimental study [10–14] including the discovery of

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perfect as well as superlenses[15]. The elements of LHM could, artificially, be fabricated by a

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macroscopic composite of periodic or aperiodic structure, whose function is due to both the cellular architecture and the chemical composition. Nevertheless, LHM has unavoidable

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disadvantages like large loss, narrow bandwidth, metal composition, etc. Especially, metal based SRRs are corrosive, and inflexible in nature. In so far, the electromagnetic properties of non-

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metal based SRRs such as nano-carbon composition is not revealed in the literature. They are simple to fabricate, and pattern, moreover, relatively cost effective compared to lithographically obtained metal SRRs.

In the present communication, we have revealed ferro-nano-carbon (FNC) SRRs as a bianisotropic LHM for its application as an electromagnetic cloak operational at 8.5-10 GHz (Xband) regime. The FNC, prepared by the pyrolysis of camphor with variable wt % of Cobalt 4

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(Co), was studied for its structure-property relationship using electron microscopy, Raman, dielectric relaxation spectroscopy, and VSM. In analysis, formation of Co-sp3 phase, emergence of low frequency polarization modes, and enhanced internal magnetic fields were found to be

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advantageous to implement FNC as SRRs. They offered peculiar characteristic of constitutive parameters extracted using Nicolson-Ross-Weir and retrieval technique revealing bianisotropic LHM behavior of SRRs. The computational electromagnetic work indicated concealing of

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radiated field at SRRs generating a cloak-like response over the sub-wavelength (8.5-10 GHz) regime. The theoretical result resembles with the experimentally obtained scalar microwave

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scattering parameters to a certain extent. Details are presented.

2. Experimental

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2.1 Preparation of NC and FNC

The commercially available 1,7,7-trimethyl-bicycloheptan (C10H16O, camphor) of analytical

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grade was taken as the starting material to grow nano-carbon (NC). To incorporate Co in NC, various wt % (3-20) of Co(C2H3O2)2 salt was added in camphor precursor, fabricated pellets, and

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kept in the bottles are as shown in Figure 1(a). The deposition was carried out under normal thermodynamic conditions on copper and silicate substrates. The production schematic is shown in Figure 1 (b) and details are provided in ref.[16].

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production scheme of NC/FNC.

2.2 Characterizations on NC and FNC

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Figure 1. (a) Fabricated NC and FNC precursor with various wt % of Co(C2H3O2)2, (b)

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The deposited NC/FNC specimen was collected by gently scrubbing the substrate using a razor

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and VNA measurements.

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blade. These samples were subjected to electron microscopy, Raman, dielectric studies, VSM,

Morphological measurements. Surface morphology of the samples was investigated using a field

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emission scanning electron microscopy (FESEM; Zeiss Sigma), at beam potential of 5 kV. In another investigation, high-resolution transmission electron microscopy (HRTEM, G220STwin, Tecnai, FEI, USA) measurements were performed, using beam potential of 300 kV. Raman spectroscopy. Vibration spectroscopy measurements were carried out using Raman spectrometer (LABRAM HR-800) at 532 nm excitation wavelength. The resolution of the system was 4 cm-1. To confirm reproducibility of measured spectrum, several sites were examined for NC/FNC. 6

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Dielectric measurements. The dielectric relaxation studies were performed to measure the permittivity and conductivity of the samples, over 10 mHz to 30 MHz. The dielectric spectrometer (Novocontrol broadband) equipped with an analyzer (Alpha-A) interfaced to the

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sample cell was used along with Win Fit software.

VSM studies. The magnetization measurements were performed using 16 T PPMS-VSM, Quantum Design, magnetometer having dc-sensitivity 10-5 emu at 1 T with temperature range 2-

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300 K with field sweep 100 Oe/sec. The thermo-magnetic measurements (cooling/heating) were

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carried out at a rate of 1.5 K/min.

2.3 Preparation of NC and FNC split ring resonators (SRRs)

Initially, FR4 dielectric substrate was cut into 2.286 (a) × 1.016 (b) × 0.1 (d) cm3 dimension

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(Figure 2). The composite of NC/FNC was made with the help of readily available, standard

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colloidal silver liquid for imprinting SRRs onto the substrate. The fabricated SRRs consisted of a planar set of two concentric conducting rings with inner ring diameter 5 and outer 8 mm

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(thickness ~ 100 µm) having a gap (split, g = 1mm) on each ring opposite to each other.

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Figure 2. Configurations of principal axis and geometry of the FNC SRR unit cell. The field

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directions and propagation vector . Lm = 8mm, w = 0.5mm, g = 1mm, d = 1mm (thickness of the FR4 substrate), a = 22.86mm (height), b = 10.16mm (width), c = 9.78mm (distance from the

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input and output port)

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Figure 2 shows co-ordinate variables along with the geometry and the sample axis of FNC SRR unit cell. It was assumed that, three co-ordinate axis ̂ ̂ ̂ of the unit cell oriented in the z, x, y directions respectively.

Computational electromagnetics. To simulate field scattered

from SRRs, RF module of

COMSOL Multiphysics 5.2 was used by employing harmonic propagation analysis mode and parametric solver in X-band regime. In our analysis, the longitudinal configuration was assumed 8

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for the propagation of the wave. The configuration was homogenized and completely fills the was propagating in the z direction

cross section of the waveguide. The fundamental mode

modes was supported by the longitudinal configuration changing

) only

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from air (

with x and y to simulate radiated field around SRRs and microwave (scattering) S-parameters. Microwave measurements. Experimental X-Band (8–12 GHz) measurements were performed using PNA network analyzer (Agilent, N5222A), equipped with waveguide (dim. 2.3 × 1.1 cm2),

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for measuring S-parameters of NC/FNC SRRs. Prior to measurements, microwave source was

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started for 2 h for stabilization. Full two port calibration was performed on the test specimen to avoid errors due to directivity, isolation, source, load match, etc. S-parameters were determined from two port measured scattering data with the help of commercially available Agilent software module 85071, based on the procedure given in Agilent product note. The cellular structures were mounted into a quarter wave plate slot to perform measurements. Set up is shown in Figure

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S1, in the supplementary information.

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From measured S-parameters, values of permittivity and permeability were obtained using Nicolson-Ross-Weir method. Moreover, using self-consistent approach, other parameters like , forward and backward normalized wave impedances, permeability,

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refractive index,

reflection coefficients, T

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permittivity, S11 and S21 were extracted by estimating propagation factor,

phase constant in z direction, using more advanced retrieval technique.

3. Results and Discussion

The analysis has been carried out on the structure-property relationship of NC and FNC that were subsequently implemented as a composite material for SRRs. 9

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3.1 Morphological analysis of NC and FNC

Figure 3. (a) SEM at high magnification of NC randomly dispersed on silica and (b), (c), (d),

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respectively, 3, 5, 20 wt % of Co in NC (scale bar 30 nm). The inset shows EDAX of corresponding samples. Elemental composition in at % is indicated for carbon and Co. Scanning electron microscopy (SEM) exhibits the feature of NC and FNC. In Figure 3 (a) it is observed that NC clusters are randomly distributed on SiO2. The individual cluster of NC seems to be having less aggregation compared to FNCs, seen in Figure 3 (b)-(d). Though not quantified, analytically, cluster size is increasing gradually. This indicates that, in FNCs with a higher 10

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concentration of Co the tendency of formation of NC aggregate is enhanced. The clusters are random in shape and size having an arbitary number of FNCs connected. It also indicates the formation of larger 3D networks with higher Co wt %. As such, it is challenging to comment on

qualitatively, understood by studying HR-TEM.

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the crystallinity of NC and FNCs using SEM, however, nature of amorphization can be,

The HR-TEM image analysis, in Figure 4, indicated that the structures are spherical shaped

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coagulated NC. The deposited spherical NC soot having dimensions ~ 40-50 nm, consisted of concentric shells and at several sites large amount of amorphous phase is observed. Especially, at

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higher Co wt %, the top spherical surface was observed to be crystalline compared to core amorphized zone. At 20 wt % FNC, a clear demarcation between surface crystalline and core amorphous zone was observed. At several sites, we have seen crystalline outer shells separated from core FNCs by amorphous zone. The FNCs has formed three dimension structures with

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homogeneous particle size distribution. The analysis of electron microscopy revealed that, the

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obtained particles were having homogeneous isotropic structural properties. They consisted of hybrid phases i.e. crystalline as well as amorphous distributed uniformly within the structures.

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Such material can easily be transformed into a coating on the desired substrate. Though electron microscopy provides qualitative information about crystallinity, Raman spectroscopy is a

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versatile tool to quantify the phase separation in carbon. The great versatility of FNC arises from the strong dependence of their physical properties on the ratio of sp2 and sp3 bonds.

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Figure 4. Recorded HRTEM images for (a) NC, (b) 3, (c) 5, and (d) 20 wt % FNC. The inset

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shows corresponding SAED pattern of NC and FNC.

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3.2 Molecular characteristic of NC and FNC: Raman analysis

Figure 5 (a) shows recorded Raman spectrum of NC, which consisted of two peaks, D and G. They were, respectively, assigned to sp3 and sp2 phases of NC. The emergence of these phases is a peculiar characteristic of amorphous carbon indicative of a large amount of disorder.[16] To quantify this, a curve fitting was carried out in terms of spectroscopic parameters such as peak position, peak width, line shape (i.e. Gaussian, Lorentzian or a mixture of both), and band 12

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intensity using Labspecs 5.0 software. The result of the line decomposition is indicated in Figure 5. Several fits were tried living all spectroscopic parameters free to progress and the best fitting

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was invariably obtained for all recorded spectra.

Figure 5. Raman spectra recorded for (a) NC and (b) FNC 20 % at 532 nm excitation wavelength.

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For NC, D-peak was deconvoluted for two components at 1313.31 and 1353.97 cm-1 having

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effective peak width ~ 110 cm-1. In the case of FNC, the major change that has been observed in recorded spectra was variations in line shape and width of D-peak, as seen in Figure 5 (b). For

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FNC, the effective width was increased to ~ 150 cm-1. It consisted of D-peak doublet appearing

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at 1303.99 and 1352.09 cm-1. However, the G-peak appearing in NC and FNC was found to be invariant in peak position and width, respectively, recorded to be ~ 1590 and ~ 60 cm-1. Broadly, it seems that, Co incorporated in the sp3 zone of NC. The packing fraction of sp3 is low compared to the sp2 network. Due to this, the incorporated Co gets an opportunity to migrate into the interstitial space of the sp3 zone, available within NC. This has implication on molecular and, consequently, dielectric characteristics of NC and FNC. The dielectric characteristic is associated with relaxation behavior of NC, in terms of motion of sp2 and sp3 molecules which subsequently 13

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may get modify by adding Co. Since most of the carbonaceous medium exhibit more than one dielectric molecular relaxation region, generally, no single molecular model is adequate to describe the behavior over a wide frequency and temperature range. Here, we have conducted

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frequency relaxation study mainly.

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3.3 Dielectric response of NC and FNC

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Figure 6. Recorded log-log plots for (a) permittivity and (b) ac conductivity (σac) as a function of

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frequency in the range 10 mHz to 30 MHz.

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To study molecular relaxation in NC and FNC, the equal amount powder was mixed with a polymer whose relaxation behavior is known and non-overlapping with our NC [17]. Figure 6 (a) shows variation in permittivity (in arbitrary units) as a function of frequency. It indicates very prominent low-frequency orientational polarization appeared between mHz to Hz. The observed peak could be attributed to, mainly, chair-to-chair motion of sp2 segments of NC. The incorporation of Co (3%) showed a broadening of the low-frequency peak and the trend was quite systematic with subsequent increase of Co % in NC, showing the emergence of broader 14

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shoulder peak for FNC 20 %. Figure 6 (b) shows variations in σac as a function of frequency which corresponds to dielectric loss component. At higher frequency, ranging from kHz to MHz, no prominent change has been observed for NC and FNCs. This indicates that, the electronic

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polarization is not affected as significantly as that of orientation polarization. This is consistent with the Raman data analyzed before indicating interstitial encaging of Co in NC, mainly affecting molecular environment associated with the sp3 carbon. Co is magnetic in nature. The

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encaged Co in sp3 clusters of NC though show peculiar dielectric properties, one needs to investigate the magnetic parameters of FNC, as well. This is important from the viewpoint of

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effective permeability that depends on the magnetization of the medium.

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3.4 Magnetization analysis: NC and FNC

Figure 7. (a) Magnetization hysteresis curves (M-H) measured for NC and FNC at 300 K. Inset photograph shows the response of FNC 20 % to permanent magnet, (b) M-T curve recorded for NC(inset) and FNC 20%.

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Figure 7 (a) shows M-H curves recorded for NC and FNC. The hysteresis curve recorded for NC exhibit no saturation behavior. To estimate saturation level of magnetic moment, Ms, the geometrical projection of M-H curve was taken on the magnetic moment axis. The value of Ms

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was estimated to be ~ 3.1 × 10-3 emu/g for NC. As the wt % of Co increases in NC, the value of Ms was observed to be increased, subsequently. For FNC 20 %, the Ms was obtained to be 2.03 emu/g which is three orders magnitude high compared to NC. The effective permeability, µeff,

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was computed using the values of Ms obtained for all the samples. The µeff was found to be 0.0015 µB and 10 µB, respectively, for NC and FNC 20 % [18]. There is about four orders of

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magnitude difference in effective permeability of FNC compared to NC. This showed that, the extent of internal magnetic field was more than thousand atoms in FNC, whereas, in NC the field dies by a factor of (1/6)th within the carbon sub-lattice. The schematic shown below in Figure 8

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indicate variation in effective permeability as a function of lattice distance.

Figure 8. Schematic representation of decay and rise in effective permeability with superlattice distance for NC and FNC.

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The thermomagnetic analysis, carried out using FC-ZFC measurements, on NC (inset) and FNC 20 % is shown in Figure 7 (b). From the inset, one can see that, the exchange anisotropy involved in NC medium was smaller compared to FNC 20 %. This indicates that, the inherent

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structural defects (vacancies), topological disorder, and impurities influenced exchange anisotropy. Mostly, they exist in the form of radical spin moment available on the carbon atom. Since such structural inhomogeneities are randomly spaced with smaller concentration, the

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interaction between them is indirect and assisted by a carbon sub-lattice mediator. The dipole moment induced by encaged Co in FNC play the crucial role as a mediator. The Coulomb

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interaction between itinerant sp3 electrons and magnetic dipole ensures a means for the dominant exchange interaction between the magnetic moments. Thus, significant irreversibility has been observed causing large exchange anisotropy in FNC 20 %. It would be of interest to investigate the nature of magnetization, range of ordering and correlation of ordering, however, it is in

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purview of the present discussions.

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By and large, the Co-sp3 molecular magnetic environment is responsible for generating a lowfrequency dipolar field which is highly anisotropic, inhomogeneous and distributed

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nonuniformly within sp2 nano-carbon framework. Though the atomic and molecular character of FNC seems to be advantageous, however, provide rather restrictive values of constitutive

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parameters to build a material with peculiar electric and magnetic properties, especially, at frequencies in the gigahertz range. To exploit naturally unavailable properties of FNC, they are implemented in the form of SRRs, as described in experimental (section 2.3).

3.5 Modeling and simulation: FNC SRRs

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The transformation of FNC into SRRs is a small step to replace the atoms of the original concept with the structure on a larger scale. The periodic structure was having a unit cell of a characteristic dimension a, which obeyed the scattering wave relation

⁄ .

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The electromagnetic resonance response of FNC SRRs has been investigated, numerically. Port boundary conditions were placed on the input and the output boundaries of the waveguide. For

̅ , relative permeability,

)

(

)

relative permittivity,

, total current,

, ac conductivity.

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where,

(

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the input, incident transverse electric field (TE10 mode, ̅ ) obeys Maxwell’s wave equation:

The dispersion of incident wave vector, k, is given by,

The total time reversal electric field solution is given by,

is total electric field,

)}

{

(

)}

and

corresponding incident and reflected components,

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where,

(

D

{

respectively. The related boundary condition used in terms of Poynting vector (dimension:

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energy/area × time) is given by,

| |

|

|

|

|

where, dΩ, is the volume element through which scattering occurs at SRRs. In above equation, the first term is associated with the input and the second term with the output port. The port boundary automatically determined reflection and transmission characteristics in terms of Sparameters. In Figure 9, the electric field distribution, in x-y plane, is simulated for a typical FNC 20 % SRRs unit cell, that indicated squeezing and localization of incident field around the 18

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cell. It has frequency dependence which comes through the capacitive action that was generated by SRRs. On interaction with incident field, the structure acts as an infinitely conducting cylinder in the high-frequency limit that generates oppositely directed alternating currents, due to

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split, moving within the ring structure. The curl of currents was responsible for producing a net dipole moment vector orthogonal to the plane of the ring. Thus, the imprinted SRRs together with its split acted as an LC circuit [19,20]. Over the bandwidth (8-12 GHz), the resonance

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response due to dipole moment was observed to be varied as seen in Figure 9.

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Figure 9. Simulated electric field, in x-y plane, by FNC 20 % SRRs unit cell indicating variations in the topology of the field in which (a), (b), (c), and (d) are, respectively, for 8, 8.5, 10, and 12 GHz response frequency.

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3.6 Microwave scattering and constitutive parameters: Nicolson-Ross-Weir and retrieval technique analysis Further, the simulated scalar S-parameters for FNC 20 % SRRs is shown in Figure 10 (a). The

[21], ]

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[

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magnitude S-parameters in terms of shielding effectiveness (SE) measured in dB is given by

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Figure 10. (a) simulated and (b) experimental S-parameters for FNC 20 % SRRs for X-band

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region. Inset indicate corresponding simulated and experimentally fabricated SRRs unit cell.

From computational techniques, S11 parameter was well below - 20 dB at ~ 8.5 GHz, whereas,

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at the same frequency the S21 was nearing to 0 dB. This indicated that, at this frequency, the SRRs was fully transparent to the incident radiation by squeezing the field within the unit cell. Figure 10 (b) shows, average of the experimental microwave scattering S-parameters obtained statistically for FNC 20 % SRRs. There is a marked difference between measured and simulated S-parameters of FNC SRRs which could be attributed to factors like design of unit cell, field received and interacted within the cell, response of boundaries and interfaces. In simulated cell, 20

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these factors could be operative at the optimum level in contrast to practical one. Qualitatively, the field received in simulated cell would experience no corner reflection and losses within annular structures of SRRs. Further, simulated cell is strictly a homogeneous medium and having

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infinite mismatch at the edges and the split region. In the practical cell the condition of homogeneity of medium would be somewhat graded due to presence of magnetic impurity in inherent dielectric carbon network. Such locally inhomogeneous electromagnetic medium cannot

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be simulated that effectively. As a result, one can see the variations in simulated and experimental S-parameters, however, similarity in S11 and S21 cut-off region appeared at 10.5

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GHz.

In the current study, we have used two port rectangular waveguide method in which S11 and S22 parameters were, invariably, symmetric. This is due to the fact that, incident magnetic field perpendicular to the plane containing SSRs ring will induce magnetic excitation in the ring along

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the z axis producing electric dipole along the x axis. Further, the dipole field perpendicular to the

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slit axis i.e. x axis will cause charges of opposite polarities to accumulate over the ring yielding a magnetic dipole symmetric along z axis. Thus, for the

mode, the scattering S11 and S22

plotted |

|

|

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will be symmetric. In order to calculate total loss of incident radiation in FNC SRRs, we have | as function of frequency and provided in supporting information (Figure

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S8). The medium is less lossy over 8-10 GHz compared with high frequency regime.

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Figure 11. Extracted (a) permittivity (ɛ), (b) permeability (µ), for NC and FNC by NicolsonRoss-Weir method, (c) permittivity, refractive index (n) inset, and (d) permeability real and

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technique.

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imaginary parts, total normalized wave impedance (z), for FNC 20% SRRs obtained by retrieval

Figure 11 (a) and (b) shows estimated values of constitutive parameters by Nicolson-Ross-Weir method for NC and FNC, over X-band region. The overall response of permittivity is negative with cutoff at high frequency for all the systems and almost similar trend is observed for recorded permeability. In general, the response of dipole, atom, and electron to the harmonically oscillating electromagnetic field is such that the charge segregation is in the same direction as 22

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that of oscillating field below resonance frequency. Above resonance, the charge lag occurs due to the mass involved in segregation of polar moieties harmonically bound within the medium [22], The observed negative response suggests that FNC is LHM in nature in SRRs

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configuration. Further, Nicolson-Ross-Weir formalism is based on estimation of constitutive parameters for a homogeneous, isotropic materials, directly, by examining the measured Sparameters [23]. However, this approach has some challenges for studying metamaterial cellular

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elements due to limitation on homogenization of scattered electromagnetic field [24].

In a cellular metamaterial structure, the electromagnetic response depends on three factors: (i)

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production of magnetic dipole by generation of circulating surface current due to magnetic field interaction of incident wave with the cell, (ii) generation of electric dipoles by induction of charge densities with opposite polarities due to accumulation of charges at corners/edges of the cell, and (iii) magneto-electric field coupling. The interaction transforms the metamaterial

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property from anisotropic to bianisotropic or to chiral behavior resulting asymmetric reflection

transformed in to SRRs.

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and transmission, respectively. Mostly, metamaterials exhibits bianisotropic property when

magnetoelectric

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The bianisotropic medium can be specified by analyzing constitutive, chirality, and parameters.

They

have

different

forward

and

backward

scattering

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parameters/impedances, a wider stopband transmission spectrum, they differ in forward and backward powers, having variable reflection coefficient and magnetoelectric coupling factors. It is difficult to estimate all of them merely using S11, S22 and S21, however, in the present communication we have estimated a few of them by retrieval technique [25] using following equations: (6) 23

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(7) ;

;

(8) (9)

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;

Where, b denotes bianisotropic feature of FNC SRRs, in equations (6) and (7). The intermediate variables,

reflection coefficients, T propagation factor,

forward and backward normalized wave impedances,

refractive index were

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direction,

phase constant in z

computed for longitudinal wave propagation configuration with Lm= 8mm, for SRRs. From

magnetoelectric coupling, to determine

, and

. In order to extract ɛ, µr, µi, one has

,

from above equations.

√

) )

);

(10) (11)

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)(

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(

)(

;

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(

(

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;

(

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equations (6)-(9), it has been noted that, for two port rectangular waveguide measurements

(12) (

;

√

;

)

)

(13) (14) (15)

Using equations (13)-(15), the variations in extracted parameters can be studied as a function of frequency. In addition, values of S11 and S21 obtained from (13) – (15) as function of frequency are provided in supporting information Figure S9. Figure 10 (c) and (d), typically, shows extracted ɛ, µr, µi, n, z parameters for FNC 20%. One can see that, there is a variation in the 24

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nature of profiles obtained by both the methods. The study of constitutive parameters of FNC SRRs by retrieval technique is in its infancy stage. The results of S- and constitutive parameters, broadly, suggests that the higher anisotropy and

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out of phase response of Co-sp3 dipolar field within supra-molecular carbon domains segregate the charge in opposite direction to the oscillating incident field. Further, computationally, FNC SRRs created a resonance condition at ~ 8.5 GHz, and a tradeoff ~ 10 GHz (experimentally

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resembling as well). In this sub-band regime, the average dipolar field gets coupled strongly to

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the incident field, in somewhat reverse fashion. This sets a gradient in constitutive parameters, that made FNC as a LHM to generate cloak-like response, particularly between 8.5-10 GHz, when imprinted as SRRs. The field distribution incident on the surface of SRRs was transported uniformly across the dielectric slab and generated a cloak-like effect in this frequency regime, evidently seen in Figure 8 and S6 (supporting information).

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Our discussions revealed that, heterostructure molecular environment present in FNC is

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responsible to behave like an electromagnetic cloak in narrow X-band regime that squeezes the incident field effectively and bring out the possibility to make the object invisible. The

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transparency of an object to the radar threat spectrum at guidance and tracking range is a

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strategically important application.

4. Conclusion

We have studied electromagnetic character of ferro-nano-carbon (FNC) split ring resonators (SRRs) in X-band (8-12 GHz) region. The FNC SRRs acted as a bianisotropic left-handed material (LHM) generating a cloak-like response between 8.5-10 GHz, as revealed by analysis of the constitutive parameters. Initially, FNC was synthesized using camphor precursor (1,7,725

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trimethyl-bicycloheptan, C10H16O), by incorporating variable wt % (3-20) of Co(C2H3O2)2. To understand the structure-property correlations, the obtained FNC was subjected to electron microscopy, Raman, dielectric relaxation spectroscopy, and vibrating sample magnetometry. In

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analysis, FNCs were 40-50 nm spherical, self-assembled, interconnected three-dimensional nano-carbon network with sp2/sp3 heterostructure molecular environment in which Co was encaged within sp3 phases. The molecular relaxation studies on NC and FNC clearly indicated a

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prominent low frequency (mHz to Hz) orientation polarization attributed to chair to chair motion of sp2 segment for NC which was disappeared systematically with increasing Co content. The

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amount of magnetization was increased from 3.1 × 10-3 (NC) to 2.03 emu/g (FNC 20 %) with dramatic enhancement in effective magnetic permeability by ~ 7000 times. The exchange anisotropy of the medium was high due to random volume distribution of Co substitutional impurities that interacted indirectly with carbon lattice network. This has implication on

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microwave scattering properties of FNC when transformed into SRRs, as studied experimentally.

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The numerous parameters were extracted such as scattering (S), permittivity, permeability, forward/backward scattering impedances, magnetoelectric coupling factors, refractive index,

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phase constant, etc, using Nicolson-Ross-Weir and retrieval methods. In addition, S- parameters and field profiles were simulated, indicating concealing of radiated field at FNC SRRs with S11

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around - 20 and S21 ~ 0 dB, at 8.5 GHz. In mechanism, the incident electromagnetic wave, especially, magnetic field component, extended along the y axis, interacted with SRR structures oriented in xy plane, in waveguide configuration. It generated the circulating surface currents in structures producing a magnetic dipole due to ferro carbon phase in FNC. Moreover, rich electron characteristic associated with sp2 bonding induced charge densities with opposite polarities at corners and edges of the ring structure, developing an electrical dipole, which got 26

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coupled with the incident field. This made FNC SRRs a bianisotropic LHM generating a cloaklike response at 8.5-10 GHz. The obtained SRRs were nano-carbon based material, noncorrosive, flexible, environmental friendly, and inexpensive. The FNC SRRs showed the

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emerging possibility to generate basic building block for narrow bandwidth X-band cloak.

Acknowledgments

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We acknowledge the Defence Research and Development Organization (DRDO), Ministry of Defence, Government of India, for their financial assistance. We also acknowledge funding from

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the DRDO-DIAT program on Nanomaterials by ER&IPR, DRDO. The authors acknowledge Dr. Surendra Pal, Vice Chancellor for his support. We are also thankful to Dr. S S Datar for helping in performing VNA measurements, Dr. H.S. Panda for dielectric relaxation spectroscopy. We are

A.M. Sessler, J.M. Cornwall, B. Dietz, S. Fetter, S. Frankel, R.L. Garwin, K. Gottfried, L.

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[1]

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Highlights Ferro-nano-carbon (FNC) prepared and evaluated for its structure-property relationship.

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Study showed formation of Co-sp3 phase, low frequency polarization, and enhanced internal magnetic anisotropy.

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•

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FNC were implemented as split ring resonators (SRRs).

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Constitutive parameters analysis was done using Nicolson-Ross-Weir and retrieval

FNC SRRs acted as a bianisotropic left-handed material generating a cloak-like response

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at 8.5-10 GHz.

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•

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technique.